What

Introduction

Roman dodecahedra are complex, fist-sized, 12-sided hollow bronze "mystery objects" dating to the late Roman Empire. Wikipedia has an excellent short introduction to them here.

Despite their widespread presence across the northwestern Roman provinces, the purpose of dodecahedra has eluded researchers for centuries. 

There are about ~130 known examples in Europe of dodecahedra. About 25% of those are from Roman Britain.

What they are not

I do not think that dodecahedra were for knitting gloves, gauging spear sizes, or surveying. Nor are they for gambling or games of chance. 

Virtually all theories regarding tools or other utilitarian functions are quickly discounted because of the variation in dodecahedra. They range in size from 5cm to 11cm in diameter, and their holes and decoration also vary. Since there was no standardisation between them, they would not have been effective for measurement.

I do not believe they were suitable for gambling because they do not roll like dice. Some faces are heavier than others due to the size of the holes, making the sides imbalanced. The knobs on the vertices also impede rolling. 

Finally, they are not knitting tools. See nalbinding, a simple single-needle form of knitting from the same period, which produced tight, sturdy knits, some examples of which still survive today.

So, what are they, then?

I'm working on it ;-)